To which subset of real numbers does the following number belong: 65−−√
The number 65−−√ belongs to the subset of real numbers.
To determine the subset of real numbers to which the number √65 belongs, we need to consider the properties of real numbers.
Real numbers can be divided into several subsets, such as natural numbers, whole numbers, integers, rational numbers, and irrational numbers.
First, we need to determine if √65 is a rational or irrational number. A rational number is a number that can be expressed as the quotient, or fraction, of two integers. An irrational number cannot be expressed as a fraction and has an infinite non-repeating decimal representation.
To determine if √65 is rational or irrational, we can calculate its decimal approximation using a calculator or a mathematical software. Taking the square root of 65 gives us approximately 8.06225774829855.
Since the decimal does not terminate or repeat, it is an indication that √65 is an irrational number. Therefore, √65 belongs to the subset of irrational numbers within the set of real numbers.
To determine the subset of real numbers to which the number 65√ belongs, we need to consider the properties of real numbers and the domain of the square root function.
The square root function is only defined for non-negative real numbers. Therefore, the number inside the square root must be greater than or equal to 0.
In this case, the number inside the square root is 65. Since 65 is a positive real number, we can take its square root.
By evaluating the square root of 65, we find that it is approximately 8.06. Therefore, the number 65√ is a positive real number.
Therefore, the subset of real numbers to which the number 65√ belongs is the set of positive real numbers.
Which property is illustrated by the following statement? 2y+5=5+2y
The property that is illustrated by the statement 2y+5=5+2y is the commutative property of addition.
The commutative property of addition states that for any two real numbers a and b, the sum is the same regardless of the order of the terms. In other words, a + b = b + a.
In this case, we have 2y + 5 = 5 + 2y. Here, the terms 2y and 5 are being added in different orders, but the result is the same. This demonstrates the commutative property of addition.
Which word phrase can you use to represent the algebraic expression 12x
The word phrase that can represent the algebraic expression 12x is "twelve times x" or "the product of twelve and x".
which sum or difference is equivalent to the following expression? 4(x+3)
The expression 4(x+3) can be simplified by distributing the 4 to both terms inside the parentheses.
4(x+3) = 4*x + 4*3 = 4x + 12
Therefore, the equivalent sum or difference is 4x + 12.